Distinct Subsequences
Given a string S and a string T, count the number of distinct subsequences of T in S.
A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE"
is a subsequence of "ABCDE"
while "AEC"
is not).
Here is an example:
S = "rabbbit"
, T = "rabbit"
Return 3
.
利用动态规划:
A[i][j]表示字符串S(0,i)中,关于T(0,j)的number ofdistinct subsequences。
if(S[i-1]==T[j-1])A[i][j] = A[i-1][j-1]+A[i-1][j];
else A[i][j] = A[i-1][j];
A[i][0] = 1;
A[0][j] = 0;